The Polyakov loop correlator at NNLO and singlet and octet correlators

TL;DR

This paper computes the Polyakov loop correlator at NNLO in a specific temperature regime, relating it to singlet and octet potentials within an effective field theory framework, and revisits the Polyakov loop expectation value at NNLO.

Contribution

It provides the complete NNLO calculation of the Polyakov loop correlator and clarifies its relation to singlet and octet potentials using an effective field theory approach.

Findings

Polyakov loop correlator calculated at NNLO for certain temperature ranges.

Relation established between correlator and singlet/octet potentials.

Revised NNLO calculation of Polyakov loop expectation value.

Abstract

We present the complete next-to-next-to-leading-order calculation of the correlation function of two Polyakov loops for temperatures smaller than the inverse distance between the loops and larger than the Coulomb potential. We discuss the relationship of this correlator with the singlet and octet potentials which we obtain in an Effective Field Theory framework based on finite-temperature potential Non-Relativistic QCD, showing that the Polyakov loop correlator can be re-expressed, at the leading order in a multipole expansion, as a sum of singlet and octet contributions. We also revisit the calculation of the expectation value of the Polyakov loop at next-to-next-to-leading order.